Using thin-film standards of Al, Ag, In, Sn, Sb, and Te whose mass-thickness was determined by weighing, we investigated the accuracy of two methods of thickness measurement, both of which employ electron energy-loss spectroscopy (EELS) in a transmission electron microscope (TEM). A method based on the Kramers-Kronig sum rule was found to provide an accuracy of better than 15%, given suitable treatment of the low-energy and surface losses. The log-ratio method, based on measurement of the total and zero-loss integrals and a parameterized expression for the total-inelastic mean free path, yielded more variable accuracy: the discrepancy with weighed values was less than 5% for Al but amounted to more than 50% in the case of Se and Te.